IntervalUtils (Apache Commons Math 3.6.1 API)

java.lang.Object
- org.apache.commons.math3.stat.interval.IntervalUtils

```
public final class IntervalUtils
extends Object
```
Factory methods to generate confidence intervals for a binomial proportion. The supported methods are:
- Agresti-Coull interval
- Clopper-Pearson method (exact method)
- Normal approximation (based on central limit theorem)
- Wilson score interval
Since:

3.3

Method Summary

Methods
Modifier and Type	Method and Description
`static ConfidenceInterval`	`getAgrestiCoullInterval(int numberOfTrials, int numberOfSuccesses, double confidenceLevel)` Create an Agresti-Coull binomial confidence interval for the true probability of success of an unknown binomial distribution with the given observed number of trials, successes and confidence level.
`static ConfidenceInterval`	`getClopperPearsonInterval(int numberOfTrials, int numberOfSuccesses, double confidenceLevel)` Create a Clopper-Pearson binomial confidence interval for the true probability of success of an unknown binomial distribution with the given observed number of trials, successes and confidence level.
`static ConfidenceInterval`	`getNormalApproximationInterval(int numberOfTrials, int numberOfSuccesses, double confidenceLevel)` Create a binomial confidence interval for the true probability of success of an unknown binomial distribution with the given observed number of trials, successes and confidence level using the Normal approximation to the binomial distribution.
`static ConfidenceInterval`	`getWilsonScoreInterval(int numberOfTrials, int numberOfSuccesses, double confidenceLevel)` Create a Wilson score binomial confidence interval for the true probability of success of an unknown binomial distribution with the given observed number of trials, successes and confidence level.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Method Detail
  - getAgrestiCoullInterval
```
public static ConfidenceInterval getAgrestiCoullInterval(int numberOfTrials,
                                         int numberOfSuccesses,
                                         double confidenceLevel)
```
    Create an Agresti-Coull binomial confidence interval for the true probability of success of an unknown binomial distribution with the given observed number of trials, successes and confidence level.
    
    Parameters:
    numberOfTrials - number of trials
    numberOfSuccesses - number of successes
    confidenceLevel - desired probability that the true probability of success falls within the returned interval
    
    Returns:
    Confidence interval containing the probability of success with probability confidenceLevel
    
    Throws:
    
    NotStrictlyPositiveException - if numberOfTrials <= 0.
    
    NotPositiveException - if numberOfSuccesses < 0.
    
    NumberIsTooLargeException - if numberOfSuccesses > numberOfTrials.
    
    OutOfRangeException - if confidenceLevel is not in the interval (0, 1).
  - getClopperPearsonInterval
```
public static ConfidenceInterval getClopperPearsonInterval(int numberOfTrials,
                                           int numberOfSuccesses,
                                           double confidenceLevel)
```
    Create a Clopper-Pearson binomial confidence interval for the true probability of success of an unknown binomial distribution with the given observed number of trials, successes and confidence level.
    Preconditions:
    - numberOfTrials must be positive
    - numberOfSuccesses may not exceed numberOfTrials
    - confidenceLevel must be strictly between 0 and 1 (exclusive)
    Parameters:
    numberOfTrials - number of trials
    numberOfSuccesses - number of successes
    confidenceLevel - desired probability that the true probability of success falls within the returned interval
    
    Returns:
    Confidence interval containing the probability of success with probability confidenceLevel
    
    Throws:
    
    NotStrictlyPositiveException - if numberOfTrials <= 0.
    
    NotPositiveException - if numberOfSuccesses < 0.
    
    NumberIsTooLargeException - if numberOfSuccesses > numberOfTrials.
    
    OutOfRangeException - if confidenceLevel is not in the interval (0, 1).
  - getNormalApproximationInterval
```
public static ConfidenceInterval getNormalApproximationInterval(int numberOfTrials,
                                                int numberOfSuccesses,
                                                double confidenceLevel)
```
    Create a binomial confidence interval for the true probability of success of an unknown binomial distribution with the given observed number of trials, successes and confidence level using the Normal approximation to the binomial distribution.
    
    Parameters:
    numberOfTrials - number of trials
    numberOfSuccesses - number of successes
    confidenceLevel - desired probability that the true probability of success falls within the interval
    
    Returns:
    Confidence interval containing the probability of success with probability confidenceLevel
  - getWilsonScoreInterval
```
public static ConfidenceInterval getWilsonScoreInterval(int numberOfTrials,
                                        int numberOfSuccesses,
                                        double confidenceLevel)
```
    Create a Wilson score binomial confidence interval for the true probability of success of an unknown binomial distribution with the given observed number of trials, successes and confidence level.
    
    Parameters:
    numberOfTrials - number of trials
    numberOfSuccesses - number of successes
    confidenceLevel - desired probability that the true probability of success falls within the returned interval
    
    Returns:
    Confidence interval containing the probability of success with probability confidenceLevel
    
    Throws:
    
    NotStrictlyPositiveException - if numberOfTrials <= 0.
    
    NotPositiveException - if numberOfSuccesses < 0.
    
    NumberIsTooLargeException - if numberOfSuccesses > numberOfTrials.
    
    OutOfRangeException - if confidenceLevel is not in the interval (0, 1).

Class IntervalUtils

Method Summary

Methods inherited from class java.lang.Object

Method Detail

getAgrestiCoullInterval

getClopperPearsonInterval

getNormalApproximationInterval

getWilsonScoreInterval